Question

Many hotel chains that offer free Wi- Fi service to their customers have experienced increasing demand for Internet bandwidth and increasing costs. Marriott International would like to test the hypothesis that the proportion of customers that are carrying two Wi- Fi devices exceeds 0.60. A random sample of 120 Marriott customers found that 78 have two Wi- Fi devices. Marriott International would like to set α = 0.01. The correct hypothesis statement for this hypothesis test would be ___________________________.

		H0: π = 0.60; H1: π > 0.60.
		H0: π = 0.60; H1: π < 0.60.
		H0: π = 0.60; H1: π ≠ 0.60.
		H0: p = 0.60; H1: p > 0.60.

The critical value(s) for this hypothesis test would be ________.

		1.28
		1.645
		2.33
		1.96

Answer 1

Marriott International would like to test the hypothesis that the proportion of customers that are carrying two Wi- Fi devices exceeds 0.60 .

(i)

Since we are testing for proportion p , then hypothesis to be tested would be

H0 : p = 60     ( proportion of customers that are carrying two Wi- Fi devices may not exceeds 0.60 )

H1 : p > 60 ( proportion of customers that are carrying two Wi- Fi devices exceeds 0.60 )

So correct for this hypothesis test would be

H0: p = 0.60; H1: p > 0.60.

(ii)

To find the critical value(s) for this hypothesis test .

Now we are given α = 0.01.

under null hypothesis test statistics follow normal distribution , hence its critical value would be given by z-critical value

As for α = 0.01 , corresponding z-critical value is $z_{\alpha }$ = 2.33

Since alternative hypothesis is of " > " type , so this is one-tail test , and thus the critical value $z_{\alpha }$ will be 2.33 , i.e we reject null hypothesis if calculated test statistics value is greater than 2.33

Thus , correct option is

c) 2.33

The critical value(s) for this hypothesis test would be _2.33_ .